Standard DEB model

1. defecation feeding food faeces assimilation reserve somatic maintenance maturity maintenance  1- maturation reproduction growth maturity offspring structure Standard DEB model

2. Feeding • Feeding has two aspects • disappearance of food (for food dynamics): JX,F • appearance of substrate for metabolic processing: JX,A= JX,F • Faeces • cannot come out of an animal, because it was never in it • is treated as a product that is linked to assimilation: JP,F= yPX JX,F

3. Busy periods not only include handling but also digestion and other metabolic processing Feeding arrival events of food items fast SU binding prob. 0 time slow SU binding prob. 0 time

4. Assimilation • Definition: • Conversion of substrate(s) (food, nutrients, light) into reserve(s) • Energy to fuel conversion is extracted from substrates • Implies: products associated with assimilation (e.g. faeces, CO2) • Depends on: • substrate availability • structural (fixed part of) surface area (e.g. surface area of gut) • Consequence of strong homeostasis: • Fixed conversion efficiency for fixed composition of substrate • However, biomass composition is not fixed • many species feed on biomass

5. Assimilation food density saturation constant structural volume reserve yield of E on X

6. Reserve dynamics & allocation Increase: assimilation  structural surface area Decrease: mobilisation  reserve-structure interface Change in reserve density  structural length-1 Reserve dynamics follows from weak homeostasis of biomass = structure + reserve -rule for allocation to soma: constant fraction of mobilisation rate

7. Reserve dynamics in starving active sludge PHB density, mol/mol Data from Beun, 2001 time, h

8. Yield of biomass on substrate reserve maintenance Data from Russel & Cook, 1995 1/spec growth rate, h-1

9. -rule for allocation Ingestion  Respiration  Ingestion rate, 105 cells/h O2 consumption, g/h Length, mm Length, mm Length, mm Reproduction  Cum # of young • large part of adult budget • to reproduction in daphnids • puberty at 2.5 mm • No change in • ingest., resp., or growth • Where do resources for • reprod. come from? Or: • What is fate of resources • in juveniles? Growth: Von Bertalanffy Age, d Age, d

10. Somatic maintenance • Definition of maintenance (somatic and maturity): • Collection of processes not associated with net production • Overall effect: reserve  excreted products (e.g. CO2, NH3) • Somatic maintenance comprises: • protein turnover (synthesis, but no net synthesis) • maintaining conc gradients across membranes (proton leak) • maintaining defence systems (immune system) • (some) product formation (leaves, hairs, skin flakes, moults) • movement (usually less than 10% of maintenance costs) • Somatic maintenance costs paid from flux JE,C: •  structural volume (mosts costs), pM •  surface area (specific costs: heating, osmo-regulation), pT

11. Maturity maintenance • Definition of maturity maintenance: • Collection of processes required to maintain • current state of maturity • Maturity maintenance costs paid from flux (1-)JE,C: •  maturity • constant in adults (even if they grow) • Else: size at transition depends on history of food intake

12. Maintenance first Chlorella-fed batch cultures of Daphnia magna, 20°C neonates at 0 d: 10 winter eggs at 37 d: 0, 0, 1, 3, 1, 38 Kooijman, 1985 Toxicity at population level. In: Cairns, J. (ed) Multispecies toxicity testing. Pergamon Press, New York, pp 143 - 164 30106 cells.day-1 400 Maitenance requirements: 6 cells.sec-1.daphnid-1 300 300 number of daphnids max number of daphnids 200 200 100 100 106 cells.day-1 0 0 6 12 30 60 120 8 11 15 18 21 24 28 32 35 37 30 time, d

13. Growth Definition: Conversion of reserve(s) into structure(s) Energy to fuel conversion is extracted from reserve(s) Implies: products associated with growth (e.g. CO2, NH3) Allocation to growth: Consequence of strong homeostasis: Fixed conversion efficiency

14. Mixtures of V0 & V1 morphs volume, m3 hyphal length, mm Bacillus  = 0.2 Collins & Richmond 1962 Fusarium  = 0 Trinci 1990 time, min time, h volume, m3 volume, m3 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961 time, min time, min

15. Growth

16. Growth at constant food length, mm Von Bert growth rate -1, d time, d ultimate length, mm Von Bertalanffy growth curve:

17. Mouse goes preying 2.1c On the island Gough, the house mouse Mus musculus preys on chicks of seabirds, Tristan albatross Diomedea dabbenena Atlantic petrel Pterodroma incerta The bird weights are 250  the mouse weight of 40 g, Mice typically weigh 15 g 99% of these bird species breed on Gough and are now threatened with extinction

18. Metamorphosis The larval malphigian tubes are clearly visible in this emerging cicada They resemble a fractally-branching space-filling tubing system, according to Jim Brown, but judge yourself …. Java, Nov 2007

19. Reproduction Definition: Conversion of adult reserve(s) into embryonic reserve(s) Energy to fuel conversion is extracted from reserve(s) Implies: products associated with reproduction (e.g. CO2, NH3) Allocation to reproduction in adults: Allocation per time increment is infinitesimally small We therefore need a buffer with buffer-handling rules for egg prod (no buffer required in case of placental mode) Strong homeostasis: Fixed conversion efficiency Weak homeostasis: Reserve density at birth equals that of mother Reproduction rate: follows from maintenance + growth costs, given amounts of structure and reserve at birth

20. Reproduction at constant food 103 eggs 103 eggs Rana esculenta Data Günther, 1990 Gobius paganellus Data Miller, 1961 length, mm length, mm

21. Maturity & its maintenance DEB implementation is motivated by 4 observations 1 Contrary to age, volume at birth or puberty hardly depends on food density. So stage transitions cannot be linked to age. 2 Some species continue growing after puberty. Other species, such as birds, only reproduce well after the growth period. So stage transitions cannot be linked to size. 3 Total cumulative energy investment in development at any given size of the individual depends on food density; this can be removed by allowing for maturity maintenance. 4 Ultimate reproduction rate is a continuous function of food density This demonstrates the existence of maturity maintenance.

22. Maintenance ratio 2.5.3b

23. Extremes in relative maturity at birth in mammals 2.5.2a Didelphus marsupiales (Am opossum) ♂, ♀ 0.5 + 0.5 m, 6.5 kg At birth: <2 g; ab = 8-13 d 10-12 (upto 25) young/litter, 2 litters/a Ommatophoca rossii (Ross Seal) ♂ 1.7-2.1 m, 129-216 kg ♀ 1.3-2.2 m, 159-204 kg At birth: 1 m, 16.5 kg; ab = 270 d

24. Extremes in relative maturity at birth in birds 2.5.2b Cuculus canorus (cuckoo) ♂,♀ 115 g Egg: 3.3 g; ab = 12 d Apteryx australis (kiwi) ♂ 2.2 kg; ♀ 2.8 kg Egg: 12×8 cm, 550 g; ab = 63-92 d

25. Extremes in relative maturity at birth in fish 2.5.2c Mola mola (ocean sunfish) ♂,♀ 4 m, 1500 (till 2300) kg Egg: 3 1010 eggs in buffer At birth: 1.84 mm g; ab = ? d Feeds on jellfish & combjellies Latimeriachalumnae (coelacanth) ♂, ♀ 1.9 m, 90 kg Egg: 325 g At birth: 30 cm; ab = 395 d Feeds on fish

26. Short juvenile period 2.5.2d Lemmus lemmus (Norway lemming ) ap - ab = 12 d Hemicentetes semispinosus (streaked tenrec ) ap - ab = 35 d

27. Embryonic development Crocodylus johnstoni, Data from Whitehead 1987 embryo yolk O2 consumption, ml/h weight, g time, d time, d : scaled time l : scaled length e: scaled reserve density g: energy investment ratio ;

28. Diapauze 2.6.2c seeds of heather Calluna vulgaris can germinate after 100 year

29. Foetal development Foetes develop like eggs, but rate not restricted by reserve (because supply during development) Reserve of embryo “added” at birth Initiation of development can be delayed by implantation egg cell Nutritional condition of mother only affects foetus in extreme situations weight, g Mus musculus time, d Data: MacDowell et al 1927

30. High age at birth 2.6.2f Sphenodon punctatus (tuatara) Adult: 45-60 cm, Wm = 0.5 – 1 kg, ♂ larger than ♀ 10 eggs/litter, life span 60 - >100 a Body temp 20-25 °C, ap = 20 a, Wb = 4 g, ab = 450 d.

31. Reproduction Definition: Conversion of adult reserve(s) into embryonic reserve(s) Energy to fuel conversion is extracted from reserve(s) Implies: products associated with reproduction (e.g. CO2, NH3) Allocation to reproduction in adults: Allocation per time increment is infinitesimally small We therefore need a buffer with buffer-handling rules for egg prod (no buffer required in case of placental mode) Strong homeostasis: Fixed conversion efficiency Weak homeostasis: Reserve density at birth equals that of mother Reproduction rate: follows from maintenance + growth costs, given amounts of structure and reserve at birth

32. Reproduction at constant food 103 eggs 103 eggs Rana esculenta Data Günther, 1990 Gobius paganellus Data Miller, 1961 length, mm length, mm

33. General assumptions • State variables: structural body mass & reserve & maturity • structure reserve do not change in composition; maturity is information • Food is converted into faeces • Assimilates derived from food are added to reserves, • which fuel all other metabolic processes • Three categories of processes: • Assimilation: synthesis of (embryonic) reserves • Dissipation: no synthesis of biomass • Growth: synthesis of structural body mass • Product formation: included in these processes (overheads) • Basic life stage patterns • dividers (correspond with juvenile stage) • reproducers • embryo (no feeding • initial structural body mass is negligibly small • initial amount of reserves is substantial) • juvenile (feeding, but no reproduction) • adult (feeding & male/female reproduction)

34. Specific assumptions • Reserve density hatchling = mother at egg formation • foetuses: embryos unrestricted by energy reserves • Stage transitions: cumulated investment in maturation > threshold • embryo  juvenile initiates feeding • juvenile  adult initiates reproduction & ceases maturation • Somatic maintenance  structure volume & maturity maintenance  maturity • (but some somatic maintenance costs  surface area) • maturity maintenance does not increase • after a given cumulated investment in maturation • Feeding rate  surface area; fixed food handling time • Body mass does not change at steady state • Fixed fraction of mobilised reserve is spent on • somatic maintenance + growth (-rule) • Starving individuals: priority to somatic maintenance • do not change reserve dynamics; continue maturation, reprod. • or change reserve dynamics; cease maturation, reprod.; do or do not shrink in structure

35. Primary DEB parameters 2.8a time-length-energy time-length-mass